The overall goal of this research is to develop, implement, analyze, and evaluate new statistical methods for tomographic image reconstruction in emission computed tomography. The proposed methods improve on the conventional filtered backprojection reconstruction method, as well as the unregularized iterative methods that have recently become available commercially (for SPECT) and suffer from a variety of disadvantages, including slow convergence, noise artifacts that increase with iteration, and nonuniform spatial resolution. This proposal takes a holistic approach to improving the following interconnected components of statistical reconstruction methods: developing statistical models that are more accurate and are robust to model errors, and developing fast globally convergent iterative algorithms for maximizing the statistical objective function. Particular emphasis will be placed on investigating improved methods for reconstructing attenuation maps from transmission measurements, since errors in conventional attenuation correction methods contribute very significantly to the noise in the reconstructed emission image. This effort will focus on iterative algorithms that are suitable for large 3-D data sets by applying parallel computing using multiprocessor architectures. Although the methodology should be generally applicable in PET and SPECT, the investigators will focus on applications in the thorax and abdomen, namely PET oncologic imaging and SPECT cardiac imaging. The improved image quality that results from proper statistical modeling and less noisy attenuation correction should be of particularly significant clinical value in those applications. The proposed statistical methods for post-injection PET transmission scans will significantly improve the clinical utility of PET with delayed FDG scans.